Question

what is remainder theorom
​

Answer 1

Answer:

After dividing we get the answer 2x+1, but there is a remainder of 2. Say we divide by a polynomial of degree 1 (such as "x−3") the remainder will have degree 0 (in other words a constant, like "4").

Example: 2x2−5x−1 divided by x−3

Answer 2

Answer:

The remainder theorem states the following: If you divide a polynomial f(x) by (x - h), then the remainder is f(h). The theorem states that our remainder equals f(h). Therefore, we do not need to use long division, but just need to evaluate the polynomial when x = h to find the remainder.

Example:

Find the remainder when 4x3 – 5x + 1 is divided by

a) x – 2

b) x + 3

Solution:

Let f(x) = 4x3– 5x + 1

a) When f(x) is divided by x – 2, remainder,

R = f(2) = 4(2)3– 5(2) + 1 = 23

b) When f(x) is divided by x + 3, remainder,

R = f(–3) = 4(–3)3– 5(–3) + 1 = –92